Ubiquity of graphs with nowhere-linear end structure.

A graph is said to be -, where is the minor relation between graphs, if whenever is a graph with for all , then one also has , where is the disjoint union of many copies of . A well-known conjecture of Andreae is that every locally finite connected graph is -ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph which implies that is -ubiquitous. In particular this implies that the full-grid is -ubiquitous.